In a conventional radar device, a laser beam is irradiated, and a distance to a reflecting object is measured on the basis of a peak of a receiving signal waveform resulting from the irradiated laser beam as disclosed in US 2004/0169840 A1 (JP 2004-177350A) or US 2005/0200833 A1 (JP 2005-257405A). According to this device, a time difference (peak time) between a time at which the laser beam is emitted and a peak of the receiving signal is measured to calculate the distance to the reflecting object by the following expression.Distance=Peak time×Laser beam velocity/2  (Ex. 1)
In the case of measuring the peak time, a time difference between a time at which laser emission starts and a center (peak center) of the peak waveform of the receiving signal is calculated by conducting analog signal processing. Alternatively, the receiving signal is subjected to analog-to-digital (AD) conversion, the peak center is found in a digital manner, and a period of time after the time at which the laser emission starts is calculated.
In those calculation methods, the peak center in the digital manner is found in an integrating process for the purpose of improving the S/N ratio of the receiving signal as disclosed in US 2004/0169840 A1. The integrating process means a process of adding a given number of receiving signals from the same reflecting object. The N adding processes are conducted on the receiving signals from the same reflecting object, thereby increasing the intensity of the reflection peak by N times. Since the intensity of the random noise signal increases √N times, only the reflection peak is so emphasized as to distinguish the reflection peak from the random noise. The integrating process is effective in extracting the peak of the reflection signal with emphasis under the circumstances where the intensity of the reflection peak is low and cannot distinguish from the random noise.
In the integrating process, the receiving signal that has been converted into the digital signal by the AD conversion is integrated. This is because the receiving signals that are different in the receiving time from each other are added together in the integrating process, it is necessary to record the addition results of the past receiving signals, and the recording of the addition results can be readily realized by recording the receiving signals that have been converted into the digital signals.
FIG. 2C of US 2004/0169840A1 discloses the configuration of realizing the integrating operation by an AD converter circuit. Because the AD converter circuit realizes sampling with skipping every sampling period, the center position of the peak waveform of the receiving signal is not always sampled. Under the circumstances, in the case of using the AD converter circuit, it is necessary to estimate the center of the peak waveform on the basis of the sampling results. That is, it is necessary to extract the peak center from the waveform whose peak is emphasized by integration.
FIG. 4B of US 2004/0169840 A1 discloses a method of estimating the peak center, and FIG. 14B of US 2005/0200833 A1 (JP2005-257405) shows a specific method of estimating the peak center. A description will be given of a method of estimating the peak center with reference to FIG. 14B of US 2005/0200833 A1. As shown in US 2005/0200833 A1, a constant threshold value is first set with respect to the peak waveform that is obtained by the integrating process to obtain two cross points of the peak waveform and the threshold value. The threshold value is obtained by multiplying the maximum value of the peak waveform (maximum value of the integrated values of the AD conversion results) by a coefficient k that satisfies 0<k<1.
In order to find the cross points of the peak waveform and the threshold value, two points which are larger and smaller than the threshold value are detected. For example, the threshold value is interposed between two points of (t1, a1) and (t2, a2) in FIG. 14B at a leading portion of the peak waveform, and the threshold value is vertically interposed between two points of (t3, a3) and (t4, a4) at a trailing portion of the peak waveform.
The tx (x=1, 2, 3, 4) of (tx, ax) represents an elapsed time from a laser emission start, and is located on a sampling point of the AD conversion. Also, ax (x=1, 2, 3, 4) is an integration results of the receiving signals on the tx point. The two points between which the threshold value is interposed are connected by a line, and when cross points between the threshold value and the line on the time axis are T1 and T2, T1 and T2 are calculated by the following expression, in which Th represents a threshold.T1=(Th−a1)×(t2−t1)/(a2−a1)+t1  Ex. 2T2=(a3−Th)×(t4−t3)/(a3−a4)+t3  Ex. 3
When T1 and T2 are determined, the peak waveform center time is estimated by calculating the following expression.Peak center estimate time=(T1+T2)/2  Ex. 4
In the above conventional radar device, because the above Expression 1 is calculated on the basis of the peak center estimate time that is calculated by the above Expression 4 to measure the distance to the reflecting object, the estimate precision of the peak center estimate time is a precision of the distance calculation as it is. Therefore, in the case where the interval of the sampling point of the AD conversion is long with respect to the peak width of the peak waveform, an error in the estimate time that is calculated in the above Expression 4 becomes large.
In order to quantitatively evaluate the estimate error of the peak center estimate time, the Gauss waveform is used in a model of the peak waveform for consideration. The Gauss waveform is represented by the following expression, and is readily quantitatively dealt with.Gauss waveform (t)=exp{−a×(t−b)×(t−b)}  Ex. 5
Symbol “b” in the above Expression 5 is a parameter that gives a peak waveform center (PC) position. FIG. 8A shows models of two peak waveforms that are different in the peak center position using the Gauss waveform represented in the above Expression 5 together. In FIG. 8A, plural vertical lines that are in parallel to the axis of ordinate represent a time of the sampling point of the AD conversion. The AD conversion result outputs the peak values at points where the plural vertical lines cross the waveform. A left waveform of FIG. 8A is located at a position where the peak center PC is sampled, and a right waveform is located at a position where the peak center PC is not sampled.
The AD conversion results (dots on the graph) of the waveform shown in FIG. 8A is shown in FIG. 8B as being connected by an interpolation curve on the original waveforms. In the right peak waveform (a waveform whose peak center PC is not sampled) shown in FIG. 8B, the graph connected by the interpolation curve shown by a solid line is deviated from the original waveform shown by a dotted line. This deviation becomes more remarkable as the sampling interval becomes longer than the peak width.
The left peak waveform of FIG. 8B (waveform whose peak center is sampled) is shown in FIG. 8C together with the set threshold value (coefficient k=0.625). The threshold value on the peak leading portion of the peak waveform is interposed between two points (t1, a1) and (t2, a2), and the threshold value on the peak trailing portion is interposed between two points (t2, a2) and (t3, a3). T1 and T2 are calculated by using the values of two points at each of the two portions on the leading portion and the trailing portion of the peak waveform, and the peak center estimate time is calculated on the basis of the above Expression 4. The calculation results coincide with the actual peak center. This is because, in the case of the peak waveform shown in FIG. 8C, since the peak center is sampled by the AD conversion, the peak waveform is symmetrical with respect to the sampling point with the result that T1 and T2 are positioned symmetrically with respect to the peak center.
The right peak waveform of FIG. 8B (waveform whose peak center is not sampled) is shown in FIG. 8D together with the set threshold value (coefficient k=0.625). The threshold value on the leading portion of the peak waveform is interposed between two points (t1, a1) and (t2, a2), and the threshold value on the peak trailing portion is interposed between two points (t3, a3) and (t4, a4). T1 and T2 are calculated by using the values of two points at each of the two portions on the leading portion and the trailing portion of the peak waveform, and the peak center estimate time is calculated on the basis of the above Expression 4. As is understood from the asymmetry of the curve connected by the interpolation curve, the calculation results do not coincide with the actual peak center. Therefore, in the case of the peak waveform whose peak center is not sampled, even if the original waveform is going to be restored by connecting the sampled points, the sampling points are asymmetrical with respect to the peak center. As a result, the peak center estimate time that is estimated by calculating the above Expression 4 does not coincide with the actual peak center.